Finite Group Databasebeta

← #15749981

Subgroups — #15749981

Order 3328.

192 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114985C211yesmaximal, characteristic
2#13113139C211yesmaximal, characteristic
3C13×#2165C211yesmaximal, characteristic
4C4×C13×M16C2211yescharacteristic
5C4×#6099—21no—
6C13×#364—21no—
7C13×#349—21no—
8C13×#347C412yescomplemented
9#11718152C411yescharacteristic
10#11718149C411yescharacteristic
11#11718148—21no—
12#11718115—21no—
13#11718047C411yescharacteristic, complemented
14#11718046—21no—
15C8×#1055C411yescharacteristic, complemented
16C2×C13×M16C2×C411yescharacteristic
17C2×C13×M16D411yescharacteristic
18C2×C42×C13D411yescharacteristic
19#88180—21no—
20C2×#6099—22no—
21C2×#6099—21no—
22C13×M32—22no—
23C13×#97C2×C411yescharacteristic
24C13×#97Q811yescharacteristic
25C4×C8×C13C2×C411yescharacteristic
26C4×C8×C13D411yescharacteristic
27#88043—22no—
28C4×#1055—21no—
29C4×#1055—21no—
30#7225—131nomaximal, Sylow
31C22×C4×C13—21no—
32C22×C4×C13C22⋊C411yescharacteristic
33C13×M16—41no—
34C13×M16—41no—
35C2×C8×C13C4211yescharacteristic
36C2×C8×C13C22⋊C411yescharacteristic
37C2×C8×C13C4⋊C411yescharacteristic
38C2×C8×C13C4⋊C411yescharacteristic
39C42×C13—21no—
40C42×C13C22⋊C411yescharacteristic
41C42×C13C4⋊C411yescharacteristic
42C22⋊Dic13—41no—
43C4⋊Dic13—41no—
44C4×Dic13—41no—
45#6099—44no—
46#6099—41no—
47#6099—41no—
48C2×#1055—22no—
49C2×#1055—22no—
50C2×#1055—41no—
51C13×C16—42no—
52#2165D1311yescharacteristic
53#1841—131no—
54#1455—131no—
55C23×C13#10411yescharacteristic
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—42no—
61C2×C4×C13#9511yescharacteristic
62C2×C4×C13#10411yescharacteristic
63C2×Dic13—81no—
64C8×C13—21no—
65C8×C13—21no—
66C8×C13—21no—
67C8×C13—21no—
68#1055—24no—
69#1055—42no—
70#1055—81no—
71C4×M16—261no—
72C4×M16C2×D1311yescharacteristic
73#364—21no—
74#349—21no—
75#347Dic1312yescomplemented
76#344—261no—
77#339—261no—
78#338—131no—
79H(3,ℤ/4)—131no—
80#322—131no—
81#322—261no—
82C82—131no—
83C22×C13—21no—
84C22×C13—41no—
85C22×C13#33911yescharacteristic
86C4×C13—22no—
87C4×C13—21no—
88C4×C13—41no—
89C4×C13H(3,ℤ/4)11yescharacteristic
90C4×C13#34411yescharacteristic
91Dic13—161no—
92C2×M16—262no—
93C2×M16—261no—
94C2×M16C4×D1311yescharacteristic
95C2×M16C22⋊D1311yescharacteristic
96#117—261no—
97C2×C42D5211yescharacteristic
98M32—22no—
99#97—262no—
100#97Dic2611yescharacteristic
101#97C2×Dic1311yescharacteristic
102C4×C8—261no—
103C4×C8—261no—
104C4×C8C4×D1311yescharacteristic
105C4×C8C22⋊D1311yescharacteristic
106C2×C13—21no—
107C2×C13—41no—
108C2×C13#128811yescharacteristic
109C22×C4—21no—
110C22×C4#610311yescharacteristic
111M16—41no—
112M16—41no—
113M16—524no—
114M16—521no—
115M16—521no—
116C2×C8—262no—
117C2×C8—262no—
118C2×C8—521no—
119C2×C8C4×Dic1311yescharacteristic
120C2×C8#610111yescharacteristic
121C2×C8#610111yescharacteristic
122C2×C8C22⋊Dic1311yescharacteristic
123C4⋊C4—521no—
124C22⋊C4—521no—
125C42—21no—
126C42—521no—
127C42C4⋊Dic1311yescharacteristic
128C42#610311yescharacteristic
129C16—42no—
130C13#722511yescharacteristic, complemented, Sylow
131C23#8806511yescharacteristic
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—42no—
137C2×C4—1041no—
138C2×C4#8806511yescharacteristic
139C2×C4#8807111yescharacteristic
140C8—21no—
141C8—21no—
142C8—21no—
143C8—21no—
144C8—264no—
145C8—522no—
146C8—1041no—
147C22—21no—
148C22—41no—
149C22#1171814711yescharacteristic
150C4—22no—
151C4—21no—
152C4—41no—
153C4—2081no—
154C4#1171812311yescharacteristic
155C4#1171815111yescharacteristic
156C2—21no—
157C2—41no—
158C2#1311270211yescharacteristic
subgroupG/H
centerC4#11718123
commutatorC2×C8×C13C42
FrattiniC4×M16C2×D13
FittingC13×#2165C2
socleC2×C13#1288
prime radicalC23×C13#104
cosocleC4×C13×M16C22
hypercenter#2165D13
hypocenterC13#7225
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #2165

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
8. C13×#347C4semidirect
13. #11718047C4semidirect
15. C8×#1055C4semidirect
75. #347Dic13semidirect
130. C13#7225semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131149852
#131131392
C13×#21652
#722513